Multi-channel integrated photonic wavelength demultiplexer

ABSTRACT

A multi-channel photonic demultiplexer includes an input region to receive a multi-channel optical signal including four distinct wavelength channels, four output regions, each adapted to receive a corresponding one of the four distinct wavelength channels demultiplexed from the multi-channel optical signal, and a dispersive region optically disposed between the input region and the four output regions. The dispersive region includes a first material and a second material inhomogeneously interspersed to form a plurality of interfaces that each correspond to a change in refractive index of the dispersive region and collectively structure the dispersive region to optically separate each of the four distinct wavelength channels from the multi-channel optical signal and respectively guide each of the four distinct wavelength channels to the corresponding one of the four output regions.

TECHNICAL FIELD

This disclosure relates generally to photonic devices, and in particularbut not exclusively, relates to optical multiplexers and demultiplexers.

BACKGROUND INFORMATION

Fiber-optic communication is typically employed to transmit informationfrom one place to another via light that has been modulated to carry theinformation. For example, many telecommunication companies use opticalfiber to transmit telephone signals, internet communication, and cabletelevision signals. But the cost of deploying optical fibers forfiber-optic communication may be prohibitive. As such, techniques havebeen developed to more efficiently use the bandwidth available within asingle optical fiber. Wavelength-division multiplexing is one suchtechnique that bundles multiple optical carrier signals onto a singleoptical fiber using different wavelengths.

BRIEF DESCRIPTION OF THE DRAWINGS

Non-limiting and non-exhaustive embodiments of the invention aredescribed with reference to the following figures, wherein likereference numerals refer to like parts throughout the various viewsunless otherwise specified. Not all instances of an element arenecessarily labeled so as not to clutter the drawings where appropriate.The drawings are not necessarily to scale, emphasis instead being placedupon illustrating the principles being described.

FIG. 1 is a functional block diagram illustrating a system for opticalcommunication between two optical communication devices via an opticalsignal, in accordance with an embodiment of the present disclosure.

FIGS. 2A and 2B respectively illustrate an example demultiplexer andmultiplexer, in accordance with an embodiment of the present disclosure.

FIG. 2C illustrates an example distinct wavelength channel of amulti-channel optical signal, in accordance with an embodiment of thepresent disclosure.

FIGS. 3A-3D illustrate different views of an example photonicdemultiplexer, in accordance with an embodiment of the presentdisclosure.

FIGS. 4A-4B illustrate a more detailed cross-sectional view of adispersive region of an example photonic demultiplexer, in accordancewith an embodiment of the present disclosure.

FIG. 5 is a functional block diagram illustrating a system forgenerating a design of a photonic integrated circuit, in accordance withan embodiment of the present disclosure.

FIG. 6A illustrates a demonstrative simulated environment describing aphotonic integrated circuit, in accordance with an embodiment of thepresent disclosure.

FIG. 6B illustrates an example operational simulation of a photonicintegrated circuit, in accordance with an embodiment of the presentdisclosure.

FIG. 6C illustrates an example adjoint simulation within the simulatedenvironment by backpropagating a loss value, in accordance with anembodiment of the present disclosure.

FIG. 7A is a flow chart illustrating example time steps for operationaland adjoint simulations, in accordance with an embodiment of the presentdisclosure.

FIG. 7B is a chart illustrating a relationship between gradientsdetermined from an operational simulation and an adjoint simulation, inaccordance with an embodiment of the present disclosure.

FIG. 8 shows an example method for generating a design of a photonicintegrated circuit, in accordance with an embodiment of the presentdisclosure.

DETAILED DESCRIPTION

Embodiments of photonic integrated circuits, including a multi-channelphotonic demultiplexer, as well as a method for generating a design ofphotonic integrated circuits are described herein. In the followingdescription numerous specific details are set forth to provide athorough understanding of the embodiments. One skilled in the relevantart will recognize, however, that the techniques described herein can bepracticed without one or more of the specific details, or with othermethods, components, materials, etc. In other instances, well-knownstructures, materials, or operations are not shown or described indetail to avoid obscuring certain aspects.

Reference throughout this specification to “one embodiment” or “anembodiment” means that a particular feature, structure, orcharacteristic described in connection with the embodiment is includedin at least one embodiment of the present invention. Thus, theappearances of the phrases “in one embodiment” or “in an embodiment” invarious places throughout this specification are not necessarily allreferring to the same embodiment. Furthermore, the particular features,structures, or characteristics may be combined in any suitable manner inone or more embodiments.

Wavelength division multiplexing and its variants (e.g., densewavelength division multiplexing, coarse wavelength divisionmultiplexing, and the like) take advantage of the bandwidth of opticalfibers by bundling multiple optical carrier signals onto a singleoptical fiber. Once the multiple carrier signals are bundled together,they are transmitted from one place to another over the single opticalfiber where they may be demultiplexed to be read out by an opticalcommunication device. However, devices that decouple the carrier signalsfrom one another remain prohibitive in terms of cost, size, and thelike.

Moreover, design of photonic devices, such as those used for opticalcommunication, are traditionally designed via conventional techniquessometimes determined through a simple guess and check method ormanually-guided grid-search in which a small number of design parametersfrom pre-determined designs or building blocks are adjusted forsuitability to a particular application. However, in actuality, thesedevices may have design parameters ranging from hundreds all the way tomany billions or more, dependent on the device size and functionality.Thus, as functionality of photonic devices increases and manufacturingtolerances improve to allow for smaller device feature sizes, it becomesincreasingly important to take full advantage of these improvements viaoptimized device design.

Described herein are embodiments of a photonic integrated circuit (e.g.,a multi-channel photonic demultiplexer and/or multiplexer) having adesign obtainable by an inverse design process. More specifically,techniques described in embodiments herein utilize gradient-basedoptimization in combination with first-principle simulations to generatea design from an understanding of the underlying physics that areexpected to govern the operation of the photonic integrated circuit. Itis appreciated in other embodiments, design optimization of photonicintegrated circuits without gradient-based techniques may also be used.Advantageously, embodiments and techniques described herein are notlimited to conventional techniques used for design of photonic devices,in which a small number of design parameters for pre-determined buildingblocks are adjusted based on suitability to a particular application.Rather, the first-principles based designs described herein are notnecessarily dependent on human intuition and generally may result indesigns which outstrip current state-of-the-art designs in performance,size, robustness, or a combination thereof. Further still, rather thanbeing limited to a small number of design parameters due to conventionaltechniques, the embodiments and techniques described herein may providescalable optimization of a nearly unlimited number of design parameters.

FIG. 1 is a functional block diagram illustrating a system 100 foroptical communication (e.g., via wavelength division multiplexing orother techniques) between optical communication devices 101-A and 101-Bvia optical signal 110, in accordance with an embodiment of the presentdisclosure. More generally, optical communication device 101-A isconfigured to transmit information by modulating light from one or morelight sources into a multi-channel optical signal 110 (e.g., a singularoptical signal that includes a plurality of distinct wavelengthchannels) that is subsequently transmitted from optical communicationdevice 101-A to optical communication device 101-B via an optical fiber,a light guide, a wave guide, or other photonic device. Opticalcommunication device 101-B receives the multi-channel optical signal 110and demultiplexes each of the plurality of distinct wavelength channelsfrom the multi-channel optical signal 110 to extract the transmittedinformation. It is appreciated that in some embodiments opticalcommunication devices 101-A and 101-B may be distinct and separatedevices (e.g., an optical transceiver or transmitter communicativelycoupled via one or more optical fibers to a separate optical transceiveror receiver). However, in other embodiments, optical communicationdevices 101-A and 101-B may be part of a singular component or device(e.g., a smartphone, a tablet, a computer, optical device, or the like).For example, optical communication devices 101-A and 101-B may both beconstituent components on a monolithic integrated circuit that arecoupled to one another via a waveguide that is embedded within themonolithic integrated circuit and is adapted to carry optical signal 110between optical communication devices 101-A and 101-B or otherwisetransmit the optical signal between one place and another.

In the illustrated embodiment, optical communication device 101-Aincludes a controller 105, one or more interface devices 107 (e.g.,fiber optic couplers, light guides, waveguides, and the like), amultiplexer (mux), demultiplexer (demux), or combination thereof 109,one or more light sources 111 (e.g., light emitting diodes, lasers, andthe like), and one or more light sensors 113 (e.g., photodiodes,phototransistors, photoresistors, and the like) coupled to one another.The controller includes one or more processors 115 (e.g., one or morecentral processing units, application specific circuits, fieldprogrammable gate arrays, or otherwise) and memory 117 (e.g., volatilememory such as DRAM and SAM, non-volatile memory such as ROM, flashmemory, and the like). It is appreciated that optical communicationdevice 101-B may include the same or similar elements as opticalcommunication device 101-A, which have been omitted for clarity.

Controller 105 orchestrates operation of optical communication device101-A for transmitting and/or receiving optical signal 110 (e.g., amulti-channel optical signal having a plurality of distinct wavelengthchannels or otherwise). Controller 105 includes software (e.g.,instructions included in memory 117 coupled to processor 115) and/orhardware logic (e.g., application specific integrated circuits,field-programmable gate arrays, and the like) that when executed bycontroller 105 causes controller 105 and/or optical communication device101-A to perform operations.

In one embodiment, controller 105 may choreograph operations of opticalcommunication device 101-A to cause light sources 103 to generate aplurality of distinct wavelength channels that are multiplexed viamux/demux 109 into a multi-channel optical signal 110 that issubsequently transmitted to optical communication device 101-B viainterface device 107. In other words, light sources 111 may output lighthaving different wavelengths (e.g., 1271 nm, 1291 nm, 1311 nm, 1331 nm,1511 nm, 1531 nm, 1551 nm, 1571, or otherwise) that may be modulated orpulsed via controller 105 to generate a plurality of distinct wavelengthchannels representative of information. The plurality of distinctwavelength channels are subsequently combined or otherwise multiplexedvia mux/demux 109 into a multi-channel optical signal 110 that istransmitted to optical communication device 101-B via interface device107. In the same or another embodiment, controller 105 may choreographoperations of optical communication device 101-A to cause a plurality ofdistinct wavelength channels to be demultiplexed via mux/demux 109 froma multi-channel optical signal 110 that is received via interface device107 from optical communication device 101-B.

It is appreciated that in some embodiments certain elements of opticalcommunication device 101-A and/or 101-B may have been omitted to avoidobscuring certain aspects of the disclosure. For example, opticalcommunication devices 101-A and 101-B may include amplificationcircuitry, lenses, or components to facilitate transmitting andreceiving optical signal 110. It is further appreciated that in someembodiments optical communication devices 101-A and/or 101-B may notnecessarily include all elements illustrated in FIG. 1. For example, inone embodiment optical communication device 101-A and/or 101-B arepassive devices that operate as an intermediary device that maypassively multiplex a plurality of distinct wavelength channels into amulti-channel optical signal 110 and/or demultiplex a plurality ofdistinct wavelength channels from a multi-channel optical signal 110.

FIGS. 2A and 2B respectively illustrate an example demultiplexer 220 andmultiplexer 250, in accordance with an embodiment of the presentdisclosure. Demultiplexer 220 and multiplexer 250 are possibleembodiments of mux/demux 109 illustrated in FIG. 1, and which may bepart of an integrated photonic circuit, silicon photonic device, orotherwise

As illustrated in FIG. 2A, demultiplexer 220 includes an input region202 and a plurality of output regions 204. Demultiplexer 220 isconfigured to receive a multi-channel optical signal 110 that includes aplurality of distinct wavelength channels (e.g., Ch. 1, Ch. 2, Ch. 3, .. . Ch. N, each having a center wavelength respectively corresponding toλ₁, λ₂, λ₃, . . . λ_(N)) via input region 202 (e.g., a waveguide thatmay correspond to interface device 107 illustrated in FIG. 1) tooptically separate each of the plurality of distinct wavelength channelsfrom the multi-channel optical signal 110 and respectively guide each ofthe plurality of distinct wavelength channels to a corresponding one ofa plurality of output regions 204 (e.g., a plurality of waveguides thatmay correspond to interface devices 107 illustrated in FIG. 1). Morespecifically, in the illustrated embodiment, each of the output regionsreceives a portion of the multi-channel optical signal that correspondsto, or is otherwise representative of, one of the plurality of distinctwavelength channels that may be output as plurality of optical signals(e.g., λ₁, λ₂, λ₃, . . . λ_(N)). The plurality of output regions mayeach be coupled to a respective light sensor (e.g., corresponding tolight sensor 113 illustrated in FIG. 1), which may be utilized toconvert the optical signals demultiplexed from the multi-channel opticalsignal 110 into electrical signals for further processing.

In the illustrated embodiment of FIG. 2B, multiplexer 250 includes aplurality of input regions 254 and an output region 252. Multiplexer isconfigured to receive a plurality of distinct optical signals (e.g., λ₁,λ₂, λ₃, . . . λ_(N)), each at a respective one of the plurality of inputregions 254 (e.g., a plurality of waveguides that may correspond tointerface devices 107 illustrated in FIG. 1). Multiplexer 250 isstructured or otherwise configured to optically combine (i.e.,multiplex) each of the plurality of distinct wavelength channels into amulti-channel optical signal 110 that is guided to output region 252(e.g., a waveguide that may correspond to interface device 107illustrated in FIG. 1). It is appreciated that in some embodiments,demultiplexer 220 illustrated in FIG. 2A and multiplexer 250 illustratedin FIG. 2B may be bidirectional such that each device may function asboth a demultiplexer and multiplexer.

FIG. 2C illustrates an example distinct wavelength channel of amulti-channel optical signal (e.g., Ch. N is multi-channel opticalsignal 110 illustrated in FIGS. 1, 2A, and 2B), in accordance with anembodiment of the present disclosure. The example channel may berepresentative of an individual channel included in a plurality ofdistinct wavelength channels of the multi-channel optical signal thatmay be demultiplexed and/or multiplexed by demultiplexer 220 of FIG. 2Aand/or multiplexer 250 of FIG. 2B. Each of the distinct wavelengthchannels may have different center wavelengths (λ_(N)) including atleast one of 1271 nm, 1291 nm, 1311 nm, 1331 nm, 1511 nm, 1531 nm, 1551nm, or 1571 nm, or otherwise. In the illustrated embodiment of FIG. 2C,the distinct wavelength channel has a channel bandwidth 212 ofapproximately 13 nm wide. However, in other embodiments the channelbandwidth may be different than 13 nm wide. Rather, the channelbandwidth may be considered a configurable parameter that is dependentupon the structure of mux/demux 107 of FIG. 1, demultiplexer 220 of FIG.2A, and/or multiplexer 250 of FIG. 2B. For example, in some embodimentseach of the plurality of distinct wavelength channels may share a commonbandwidth that may correspond to 13 nm or otherwise. Referring back toFIG. 2C, the channel bandwidth 212 may be defined as the width of apassband region 213 (i.e., the region defined as being between PB₁ andPB₂). The passband region 213 may represent an approximate powertransmission of a demultiplexer or multiplexer. It is appreciated thatin some embodiments the passband region 213 may include ripple asillustrated in FIG. 2C, which corresponds to fluctuations within thepassband region 212. In one or more embodiments, the ripple within thepassband region may be +/−2 dB or less, +/−1 dB or less, +/−0.5 dB orless, or otherwise. In some embodiments, the channel bandwidth 212 maybe defined by the passband region 212. In other embodiments, the channelbandwidth 212 may be defined as the measured power above a threshold(e.g., dB_(th)). For example, demultiplexer 220 illustrated in FIG. 2Amay optically separate channel N from multi-channel optical signal 110and have a corresponding channel bandwidth for channel N equivalent tothe range of wavelengths above a threshold value that are transmitted tothe output region 204 mapped to channel N (i.e., λ_(N)). In the same orother embodiments, isolation of the channel (i.e., defined by channelbandwidth 212) may also be considered when optimizing the design. Theisolation may be defined as a ratio between the passband region 212 andthe stopband regions (e.g., regions less than SB₁ and greater than SB₂).It is further appreciated that transition band regions (e.g., a firsttransition region between SB₁ and PB₁ and a second transition regionbetween PB₂ and SB₂) are exemplary and may be exaggerated for thepurposes of illustration. In some embodiments, optimization of thedesign of the photonic demultiplexer may also include a target metricfor a slope, width, or the like of the transition band regions.

FIGS. 3A-3D illustrate different views of an example photonicdemultiplexer 320, in accordance with an embodiment of the presentdisclosure. Photonic demultiplexer 320 is one possible implementation ofmux/demux 109 illustrated in FIG. 1 and demultiplexer 220 illustrated inFIG. 2 A. It is further appreciated that while discussion henceforth maybe directed towards photonic integrated circuits capable ofdemultiplexing a plurality of distinct wavelength channels from amulti-channel optical signal, that in other embodiments, a demultiplexer(e.g., demultiplexer 320) may also or alternatively be capable ofmultiplexing a plurality of distinct wavelength channels into amulti-channel optical signal, in accordance with embodiments of thepresent disclosure.

FIG. 3A illustrates a cross-sectional view of demultiplexer 320 along alateral plane within an active layer defined by a width 321 and a length323 of the demultiplexer 320. As illustrated, demultiplexer 320 includesan input region 302 (e.g., comparable to input region 202 illustrated inFIG. 2A), a plurality of output regions 304 (e.g., comparable toplurality of output regions 204 illustrated in FIG. 2A), and adispersive region optically disposed between the input region 302 andplurality of output regions 304. The input region 302 and plurality ofoutput regions 304 (e.g., 304-A, 304-B, 304-C, and 304-D) may each bewaveguides (e.g., slab waveguide, strip waveguide, slot waveguide, orthe like) capable of propagating light along the path of the waveguide.The dispersive region 330 includes a first material and a secondmaterial (see, e.g., FIG. 3D) inhomogeneously interspersed to form aplurality of interfaces that each correspond to a change in refractiveindex of the dispersive region 330 and collectively structure thedispersive region 330 to optically separate each of a plurality ofdistinct wavelength channels (e.g., Ch. 1, Ch. 2, Ch. 3, . . . Ch. Nillustrated in FIG. 2A) from a multi-channel optical signal (e.g.,optical signal 110 illustrated in FIG. 2A) and respectively guide eachof the plurality of distinct wavelength channels to a corresponding oneof the plurality of output regions 304 when the input region 302receives the multi-channel optical signal. In other words, input region302 is adapted to receive the multi-channel optical signal including aplurality of distinct wavelength channels and the plurality of outputregions 304 are adapted to each receive a corresponding one of theplurality of distinct wavelength channels demultiplexed from themulti-channel optical signal via dispersive region 330.

As illustrated in FIG. 3A, and more clearly shown in FIGS. 3D and 4A-4B,the shape and arrangement of the first and second material that areinhomogeneously interspersed create a plurality of interfaces thatcollectively form a material interface pattern along a cross-sectionalarea of dispersive region 330 that is at least partially surrounded by aperiphery boundary region 322 that includes the second material. In someembodiments periphery region 322 has a substantially homogeneouscomposition that includes the second material. In the illustratedembodiment, dispersive region 330 includes a first side 331 and a secondside 333 that each interface with an inner boundary (i.e., the unlabeleddashed line of periphery region 322 disposed between dispersive region330 and dashed-dotted line corresponding to an outer boundary ofperiphery region 322). First side 331 and second side 332 are disposedcorrespond to opposing sides of dispersive region 330. Input region 302is disposed proximate to first side 331 (e.g., one side of input region302 abuts first side 331 of dispersive region 330) while each of theplurality of output regions 304 are disposed proximate to second side333 (e.g., one side of each of the plurality of output regions 304 abutssecond side 333 of dispersive region 330).

In the illustrated embodiment each of the plurality of output regions304 are parallel to each other one of the plurality of output regions304. However, in other embodiments the plurality of output regions 304may not be parallel to one another or even disposed on the same side(e.g., one or more of the plurality of output regions 304 and/or inputregion 302 may be disposed proximate to sides of dispersive region 330that are adjacent to first side 331 and/or second side 333). In someembodiments adjacent ones of the plurality of output regions areseparated from each other by a common separation distance when theplurality of output regions includes t least three output regions. Forexample, as illustrated adjacent output regions 304-A and 304-B areseparated from one another by distance 306, which may be common to theseparation distance between other pairs of adjacent output regions.

As illustrated in the embodiment of FIG. 3A, demultiplexer 320 includesfour output regions 304 (e.g., 304-A, 304-B, 304-C, and 304-D) that areeach respectively mapped (i.e., by virtue of the structure of dispersiveregion 330) to a respective one of four channels included in a pluralityof distinct wavelength channels. More specifically, the plurality ofinterfaces of dispersive region 330, defined by the inhomogeneousinterspersion of a first material and a second material, form a materialinterface pattern along a cross-sectional area of the dispersion region330 (e.g., as illustrated in FIG. 3A, 4A, or 4B) to cause the dispersiveregion 330 to optically separate each of the four channels from themulti-channel optical signal and route each of the four channels to arespective one of the four output regions 304 when the input region 302regions the multi-channel optical signal.

It is noted that the first material and second material of dispersiveregion 330 are arranged and shaped within the dispersive region suchthat the material interface pattern is substantially proportional to adesign obtainable with an inverse design process, which will bediscussed in greater detail later in the present disclosure. Morespecifically, in some embodiments, the inverse design process mayinclude iterative gradient-based optimization of a design based at leastin part on a loss function that incorporates a performance loss (e.g.,to enforce functionality) and a fabrication loss (e.g., to enforcefabricability and binarization of a first material and a secondmaterial) that is reduced or otherwise adjusted via iterativegradient-based optimization to generate the design. In the same or otherembodiment, other optimization techniques may be used instead of, orjointly with, gradient-based optimization. Advantageously, this allowsfor optimization of a near unlimited number of design parameters toachieve functionality and performance within a predetermined area thatmay not have been possible with conventional design techniques.

For example, in one embodiment dispersive region 330 is structured tooptically separate each of the four channels from the multi-channeloptical signal within a predetermined area of 35 μm×35 μm (e.g., asdefined by width 325 and length 327 of dispersive region 330) when theinput region 302 receives the multi-channel optical signal. In the sameor another embodiment, the dispersive region is structured toaccommodate a common bandwidth for each of the four channels, each ofthe four channels having different center wavelengths. In one embodimentthe common bandwidth is approximately 13 nm wide and the differentcenter wavelengths is selected from a group consisting of 1271 nm, 1291nm, 1311 nm, 1331 nm, 1511 nm, 1531 nm, 1551 nm, and 1571 nm. In someembodiments, the entire structure of demultiplexer 320 (e.g., includinginput region 321, periphery region 322, dispersive region 330, andplurality of output regions 304) fits within a predetermined area (e.g.,as defined by width 321 and length 323). In one embodiment thepredetermined area is 35 μm×35 μm. It is appreciated that in otherembodiments dispersive region 330 and/or demultiplexer 330 fits withinother areas greater than or less than 35 μm×35 μm, which may result inchanges to the structure of dispersive region 330 (e.g., the arrangementand shape of the first and second material) and/or other components ofdemultiplexer 320.

In the same or other embodiments the dispersive region is structured tohave a power transmission of −2 dB or greater from the input region 302,through the dispersive region 330, and to the corresponding one of theplurality of output regions 304 for a given wavelength within one of theplurality of distinct wavelength channels. For example, if channel 1 ofa multi-channel optical signal is mapped to output region 304-A, thenwhen demultiplexer 320 receives the multi-channel optical signal atinput region 302 the dispersive region 330 will optically separatechannel 1 from the multi-channel optical signal and guide a portion ofthe multi-channel optical signal corresponding to channel 1 to outputregion 304-A with a power transmission of −2 dB or greater. In the sameor another embodiment, dispersive region 330 is structured such that anadverse power transmission (i.e., isolation) for the given wavelengthfrom the input region to any of the plurality of output regions otherthan the corresponding one of the plurality of output regions is −30 dBor less, −22 dB or less, or otherwise. For example, if channel 1 of amulti-channel optical signal is mapped to output region 304-A, then theadverse power transmission from input region 302 to any other one of theplurality of output regions (e.g., 304-B, 304-C, 304-D) other than thecorresponding one of the plurality of output regions (e.g., 304-A) is−30 dB or less, −22 dB or less, or otherwise. In some embodiments, amaximum power reflection from demultiplexer 320 of an input signal(e.g., a multi-channel optical signal) received at an input region(e.g., input region 302) is reflected back to the input region bydispersive region 330 or otherwise is −40 dB or less, −20 dB or less, −8dB or less, or otherwise. It is appreciated that in other embodimentsthe power transmission, adverse power transmission, maximum power, orother performance characteristics may be different than the respectivevalues discussed herein, but the structure of dispersive region 330 maychange due to the intrinsic relationship between structure,functionality, and performance of demultiplexer 320.

FIG. 3B illustrates a vertical schematic or stack of various layers thatare included in the illustrated embodiment of demultiplexer 320.However, it is appreciated that the illustrated embodiment is notexhaustive and that certain features or elements may be omitted to avoidobscuring certain aspects of the invention. In the illustratedembodiment, demultiplexer 320 includes substrate 302, dielectric layer304, active layer 306 (e.g., as shown in the cross-sectionalillustration of FIG. 3A), and a cladding layer 308. In some embodiments,demultiplexer 320 may be, in part or otherwise, a photonic integratedcircuit or silicon photonic device that is compatible with conventionalfabrication techniques (e.g., lithographic techniques such asphotolithographic, electron-beam lithography and the like, sputtering,thermal evaporation, physical and chemical vapor deposition, and thelike).

In one embodiment a silicon on insulator (SOI) wafer may be initiallyprovided that includes a support substrate (e.g., a silicon substrate)that corresponds to substrate 302, a silicon dioxide dielectric layerthat corresponds to dielectric layer 304, a silicon layer (e.g.,intrinsic, doped, or otherwise), and a oxide layer (e.g., intrinsic,grown, or otherwise). In one embodiment, the silicon in the active layer306 may be etched selectively by lithographically creating a pattern onthe SOI wafer that is transferred to SOI wafer via a dry etch process(e.g., via a photoresist mask or other hard mask) to remove portions ofthe silicon. The silicon may be etched all the way down to dielectriclayer 304 to form voids that may subsequently be backfilled with silicondioxide that is subsequently encapsulated with silicon dioxide to formcladding layer 308. In one embodiment, there may be several etch depthsincluding a full etch depth of the silicon to obtain the targetedstructure. In one embodiment, the silicon may be 220 nm thick and thusthe full etch depth may be 220 nm. In some embodiments, this may be atwo-step encapsulation process in which two silicon dioxide depositionsare performed with an intermediate chemical mechanical planarizationused to yield a planar surface.

FIG. 3C illustrates a more detailed view of active layer 306 (relativeto FIG. 3B) taken along a portion of periphery region 322 that includesinput region 302 of FIG. 3A. In the illustrated embodiment, activeregion 306 includes a first material 332 with a refractive index of ε₁and a second material 334 with a refractive index of ε₂ that isdifferent from ε₁. Homogenous regions of the first material 332 and thesecond material 334 may form waveguides or portions of waveguides thatcorrespond to input region 302 and plurality of output regions 304 asillustrated in FIGS. 3A and 3C.

FIG. 3D illustrates a more detailed view of active layer 306 (relativeto FIG. 3B) taken along dispersive region 330. As described previously,dispersive region 306 includes a first material 332 (e.g., silicon) anda second material 334 (e.g., silicon dioxide) that are inhomogeneouslyinterspersed to form a plurality of interfaces 336 that collectivelyform a material interface pattern. Each of the plurality of interfaces336 that form the interface pattern correspond to a change in refractiveindex of dispersive region 330 to structure the dispersive region (i.e.,the shape and arrangement of first material 332 and second material 334)to provide, at least in part, the functionality of demultiplexer 320(i.e., optical separation of the plurality of distinct wavelengthchannels from the multi-channel optical signal and respective guidanceof each of the plurality of distinct wavelength channels to thecorresponding one of the plurality of output regions 304 when the inputregion 302 receives the multi-channel optical signal).

It is appreciated that in the illustrated embodiments of demultiplexer320 as shown in FIGS. 3A-3D, the change in refractive index is shown asbeing vertically consistent (i.e., the first material 332 and secondmaterial 334 form interfaces that are substantially vertical orperpendicular to a lateral plane or cross-section of demultiplexer 330.However, in the same or other embodiments, the plurality of interfaces(e.g., interfaces 336 illustrated in FIG. 3D) may not be substantiallyperpendicular with the lateral plane or cross-section of demultiplexer330.

FIG. 4A illustrates a more detailed cross-sectional view of a dispersiveregion of example photonic demultiplexer 420, in accordance with anembodiment of the present disclosure. FIG. 4B illustrates a moredetailed view of an interface pattern formed by the shape andarrangement of a first material 432 and a second material 434 for thedispersive region of the photonic demultiplexer 420 of FIG. 4A.Demultiplexer 420 is one possible implementation of mux/demux 109illustrated in FIG. 1, demultiplexer 220 illustrated in FIG. 2A, anddemultiplexer 320 illustrated in FIGS. 3A-3D.

As illustrated in FIGS. 4A-4B, demultiplexer 420 includes an inputregion 402, a plurality of output regions 404, and a dispersive region430 optically disposed between input region 402 and plurality of outputregions 404. Dispersive region 430 is surrounded, at least in part, by aperipheral region 422 that includes an inner boundary 436 and an outerboundary 438. It is appreciated that like named or labeled elements ofdemultiplexer 420 may similarly correspond to like named or labeledelements of other demultiplexers described in embodiments of the presentdisclosure.

The first material 432 (i.e., black colored regions within dispersiveregion 430) and second material 434 (i.e., white colored regions withindispersive region 430) of photonic demultiplexer 420 are inhomogeneouslyinterspersed to create a plurality of interfaces that collectively formmaterial interface pattern 431 as illustrated in FIG. 4B. Morespecifically, an inverse design process that utilizes iterativegradient-based optimization, Markov Chain Monte Carlo optimization, orother optimization techniques combined with first principles simulationsto generate a design that is substantially replicated by dispersiveregion 430 within a proportional or scaled manner such that photonicdemultiplexer 420 provides the desired functionality. In the illustratedembodiment, dispersive region 430 is structured to optically separateeach of a plurality of distinct wavelength channels from a multi-channeloptical signal and respectively guide each of the plurality of distinctwavelength channels to a corresponding one of the plurality of outputregions 404 when the input region 402 receives the multi-channel opticalsignal. More specifically, the plurality of output regions 404-A, 404-B,404-C, and 404-D are respectively mapped to wavelength channels havingcenter wavelengths correspond to 1271 nm, 1291 nm, 1311 nm, and 1331 nm.In another embodiment, output regions 404-A, 404-B, 404-C, and 404-D arerespectfully mapped to wavelength channels having center wavelengthsthat correspond to 1511 nm, 1531 nm, 1551 nm, and 1571 nm.

As illustrated in FIG. 4B material interface pattern 431, which isdefined by the black lines within dispersive region 430 and correspondsto a change in refractive index within dispersive region 430, includes aplurality of protrusions 442. A first protrusion 442-A is formed of thefirst material 432 and extends from periphery region 422 into dispersiveregion 430. Similarly, a second protrusion 442-B is formed of the secondmaterial 434 and extends from periphery region 422 into dispersiveregion 430. Further illustrated in FIG. 4B, dispersive region 430includes a plurality of islands 444 formed of either the first material432 or the second material 434. The plurality islands 442 include afirst island 442-A that is formed of the first material 432 and issurrounded by the second material 434. The plurality of islands 442 alsoincludes a second island 442-B that is formed of the second material 434and is surrounded by the first material 434.

In some embodiments, material interface pattern 431 includes one or moredendritic shapes, wherein each of the one or more dendritic shapes aredefined as a branched structure formed from first material 432 or secondmaterial 434 and having a width that alternates between increasing anddecreasing in size along a corresponding direction. Referring back toFIG. 4A, for clarity, dendritic structure 446 is labeled with a whitearrow having a black border. As can be seen, the width of dendriticstructure 446 alternatively increases and decreases in size along acorresponding direction (i.e., the white labeled arrow overlaying alength of dendritic structure 446) to create a branched structure. It isappreciated that in other embodiments there may be no protrusions, theremay be no islands, there may be no dendritic structures, or there may beany number, including zero, of protrusions, islands of any materialincluded in the dispersive region 430, dendritic structures, or acombination thereof.

In some embodiments, the inverse design process includes a fabricationloss that enforces a minimum feature size, for example, to ensurefabricability of the design. In the illustrated embodiment of photonicdemultiplexer 420 illustrated in FIGS. 4A and 4B, interface pattern 431is shaped to enforce a minimum feature size within dispersive region 430such that the plurality of interfaces within the cross-sectional areaformed with first material 432 and second material 434 do not have aradius of curvature with a magnitude of less than a threshold size. Forexample, if the minimum feature size is 150 nm, the radius of curvaturefor any of the plurality of interfaces have a magnitude of less than thethreshold size, which corresponds the inverse of half the minimumfeature size (i.e., 1/75 nm⁻¹). Enforcement of such a minimum featuresize prevents the inverse design process from generating designs thatare not fabricable by considering manufacturing constraints,limitations, and/or yield. In the same or other embodiments, differentor additional checks on metrics related to fabricability may be utilizedto enforce a minimum width or spacing as a minimum feature size.

FIG. 5 is a functional block diagram illustrating a system 500 forgenerating a design of a photonic integrated circuit (i.e., photonicdevice), in accordance with an embodiment of the disclosure. System 500may be utilized to perform an inverse design process that generates adesign with iterative gradient-based optimization that takes intoconsideration the underlying physics that govern the operation of thephotonic integrated circuit. More specifically, system 500 is a designtool that may be utilized to optimize structural parameters (e.g., shapeand arrangement of a first material and a second material within thedispersive region of the embodiments described in the presentdisclosure) of photonic integrated circuits based on first-principlessimulations (e.g., electromagnetic simulations to determine a fieldresponse of the photonic device to an excitation source) and iterativegradient-based optimization. In other words, system 500 may provide adesign obtained via the inverse design process that is substantiallyreplicated (i.e., proportionally scaled) by dispersive regions 330, 430,and 472 of demultiplexers 320 and 420 illustrated in FIGS. 3A and 4A,respectively.

As illustrated, system 500 includes controller 505, display 507, inputdevice(s) 509, communication device(s) 511, network 513, remoteresources 515, bus 521, and bus 523. Controller 505 includes processor531, memory 533, local storage 535, and photonic device simulator 539.Photonic device simulator 539 includes operational simulation engine541, fabrication loss calculation logic 543, calculation logic 545,adjoint simulation engine 547, and optimization engine 549. It isappreciated that in some embodiments, controller 505 may be adistributed system.

Controller 505 is coupled to display 507 (e.g., a light emitting diodedisplay, a liquid crystal display, and the like) coupled to bus 521through bus 523 for displaying information to a user utilizing system500 to optimize structural parameters of the photonic device (i.e.,demultiplexer). Input device 509 is coupled to bus 521 through bus 523for communicating information and command selections to processor 531.Input device 509 may include a mouse, trackball, keyboard, stylus, orother computer peripheral, to facilitate an interaction between the userand controller 505. In response, controller 505 may provide verificationof the interaction through display 507.

Another device, which may optionally be coupled to controller 505, is acommunication device 511 for accessing remote resources 515 of adistributed system via network 513. Communication device 511 may includeany of a number of networking peripheral devices such as those used forcoupling to an Ethernet, Internet, or wide area network, and the like.Communication device 511 may further include a mechanism that providesconnectivity between controller 505 and the outside world. Note that anyor all of the components of system 500 illustrated in FIG. 5 andassociated hardware may be used in various embodiments of the presentdisclosure. The remote resources 515 may be part of a distributed systemand include any number of processors, memory, and other resources foroptimizing the structural parameters of the photonic device.

Controller 505 orchestrates operation of system 500 for optimizingstructural parameters of the photonic device. Processor 531 (e.g., oneor more central processing units, graphics processing units, and/ortensor processing units, etc.), memory 533 (e.g., volatile memory suchas DRAM and SRAM, non-volatile memory such as ROM, flash memory, and thelike), local storage 535 (e.g., magnetic memory such as computer diskdrives), and the photonic device simulator 539 are coupled to each otherthrough bus 523. Controller 505 includes software (e.g., instructionsincluded in memory 533 coupled to processor 531) and/or hardware logic(e.g., application specific integrated circuits, field-programmable gatearrays, and the like) that when executed by controller 505 causescontroller 505 or system 500 to perform operations. The operations maybe based on instructions stored within any one of, or a combination of,memory 533, local storage 535, physical device simulator 539, and remoteresources 515 accessed through network 513.

In the illustrated embodiment, modules 541-549 of photonic devicesimulator 539 are utilized to optimize structural parameters of thephotonic device (e.g., mux/demux 107 of FIG. 1, demultiplexer 220 ofFIG. 2A, demultiplexer 250 of FIG. 2B, demultiplexer 320 of FIGS. 3A-3D,and demultiplexer 420 of FIGS. 4A-4B). In some embodiments, system 500may optimize the structural parameters of the photonic device via, interalia, simulations (e.g., operational and adjoint simulations) thatutilize a finite-difference time-domain (FDTD) method to model the fieldresponse (e.g., electric and magnetic fields within the photonicdevice). The operational simulation engine 541 provides instructions forperforming an electromagnetic simulation of the photonic deviceoperating in response to an excitation source within a simulatedenvironment. In particular, the operational simulation determines afield response of the simulated environment (and thus the photonicdevice, which is described by the simulated environment) in response tothe excitation source for determining a performance metric of thephysical device (e.g., based off an initial description or input designof the photonic device that describes the structural parameters of thephotonic device within the simulated environment with a plurality ofvoxels). The structural parameters may correspond, for example, to thespecific design, material compositions, dimensions, and the like of thephysical device. Fabrication loss calculation logic 543 providesinstructions for determining a fabrication loss, which is utilized toenforce a minimum feature size to ensure fabricability. In someembodiments, the fabrication loss is also used to enforce binarizationof the design (i.e., such that the photonic device includes a firstmaterial and a second material that are interspersed to form a pluralityof interfaces). Calculation logic 545 computes a loss metric determinedvia a loss function that incorporates a performance loss, based on theperformance metric, and the fabrication loss. Adjoint simulation engine547 is utilized in conjunction with the operational simulation engine541 to perform an adjoint simulation of the photonic device tobackpropagate the loss metric through the simulated environment via theloss function to determine how changes in the structural parameters ofthe photonic device influence the loss metric. Optimization engine 549is utilized to update the structural parameters of the photonic deviceto reduce the loss metric and generate a revised description (i.e.,revising the design) of the photonic device.

FIGS. 6A-6C respectively illustrate an initial set up of a simulatedenvironment 601-A describing a photonic device, performing anoperational simulation of the photonic device in response to anexcitation source within the simulated environment 601-B, and performingan adjoint simulation of the photonic device within the simulatedenvironment 601-C. The initial set up of the simulated environment 201,1-dimensional representation of the simulated environment 201,operational simulation of the physical device, and adjoint simulation ofthe physical device may be implemented with system 100 illustrated inFIG. 1. As illustrated in FIGS. 6A-2C, simulated environment 601 isrepresented in two-dimensions. However, it is appreciated that otherdimensionality (e.g., 3-dimensional space) may also be used to describesimulated environment 601 and the photonic device. In some embodiments,optimization of structural parameters of the photonic device illustratedin FIGS. 6A-6C may be achieved via an inverse design process including,inter alia, simulations (e.g., operational simulations and adjointsimulations) that utilize a finite-difference time-domain (FDTD) methodto model the field response (e.g., electric and magnetic field) to anexcitation source.

FIG. 6A illustrates a demonstrative simulated environment 601-Adescribing a photonic integrated circuit (i.e., a photonic device suchas a waveguide, demultiplexer, and the like), in accordance with anembodiment of the present disclosure. More specifically, in response toreceiving an initial description of a photonic device defined by one ormore structural parameters (e.g., an input design), a system (e.g.,system 500 of FIG. 5) configures a simulated environment 601 to berepresentative of the photonic device. As illustrated, the simulatedenvironment 601 (and subsequently the photonic device) is described by aplurality of voxels 610, which represent individual elements (i.e.,discretized) of the two-dimensional (or other dimensionality) space.Each of the voxels is illustrated as two-dimensional squares; however,it is appreciated that the voxels may be represented as cubes or othershapes in three-dimensional space. It is appreciated that the specificshape and dimensionality of the plurality of voxels 610 may be adjusteddependent on the simulated environment 601 and photonic device beingsimulated. It is further noted that only a portion of the plurality ofvoxels 610 are illustrated to avoid obscuring other aspects of thesimulated environment 601.

Each of the plurality of voxels 610 may be associated with a structuralvalue, a field value, and a source value. Collectively, the structuralvalues of the simulated environment 601 describe the structuralparameters of the photonic device. In one embodiment, the structuralvalues may correspond to a relative permittivity, permeability, and/orrefractive index that collectively describe structural (i.e., material)boundaries or interfaces of the photonic device (e.g., interface pattern431 of FIG. 4B). For example, an interface 636 is representative ofwhere relative permittivity changes within the simulated environment 601and may define a boundary of the photonic device where a first materialmeets or otherwise interfaces with a second material. The field valuedescribes the field (or loss) response that is calculated (e.g., viaMaxwell's equations) in response to an excitation source described bythe source value. The field response, for example, may correspond to avector describing the electric and/or magnetic fields (e.g., in one ormore orthogonal directions) at a particular time step for each of theplurality of voxels 610. Thus, the field response may be based, at leastin part, on the structural parameters of the photonic device and theexcitation source.

In the illustrated embodiment, the photonic device corresponds to anoptical demultiplexer having a design region 630 (e.g., corresponding todispersive region 330 of FIG. 3A, and/or dispersive region 430 of FIG.4A), in which structural parameters of the physical device may beupdated or otherwise revised. More specifically, through an inversedesign process, iterative gradient-based optimization of a loss metricdetermined from a loss function is performed to generate a design of thephotonic device that functionally causes a multi-channel optical signalto be demultiplexed and guided from input port 602 to a correspondingone of the output ports 604. Thus, input port 602 (e.g., correspondingto input region 302 of FIG. 3A, input region 404 of FIG. 4A, and thelike) of the photonic device corresponds to a location of an excitationsource to provide an output (e.g., a Gaussian pulse, a wave, a waveguidemode response, and the like). The output of the excitation sourceinteract with the photonic device based on the structural parameters(e.g., an electromagnetic wave corresponding to the excitation sourcemay be perturbed, retransmitted, attenuated, refracted, reflected,diffracted, scattered, absorbed, dispersed, amplified, or otherwise asthe wave propagates through the photonic device within simulatedenvironment 601). In other words, the excitation source may cause thefield response of the photonic device to change, which is dependent onthe underlying physics governing the physical domain and the structuralparameters of the photonic device. The excitation source originates oris otherwise proximate to input port 602 and is positioned to propagate(or otherwise influence the field values of the plurality of voxels)through the design region 630 towards output ports 604 of the photonicdevice. In the illustrated embodiment, the input port 602 and outputports 604 are positioned outside of the design region 630. In otherwords, in the illustrated embodiment, only a portion of the structuralparameters of the photonic device is optimizable.

However, in other embodiments, the entirety of the photonic device maybe placed within the design region 630 such that the structuralparameters may represent any portion or the entirety of the design ofthe photonic device. The electric and magnetic fields within thesimulated environment 601 (and subsequently the photonic device) maychange (e.g., represented by field values of the individual voxels thatcollectively correspond to the field response of the simulatedenvironment) in response to the excitation source. The output ports 604of the optical demultiplexer may be used for determining a performancemetric of the photonic device in response to the excitation source(e.g., power transmission from input port 602 to a specific one of theoutput ports 604.). The initial description of the photonic device,including initial structural parameters, excitation source, performanceparameters or metrics, and other parameters describing the photonicdevice, are received by the system (e.g., system 500 of FIG. 5) and usedto configure the simulated environment 601 for performing afirst-principles based simulation of the photonic device. These specificvalues and parameters may be defined directly by a user (e.g., of system500 in FIG. 5), indirectly (e.g., via controller 505 cullingpre-determined values stored in memory 533, local storage 535, or remoteresources 515), or a combination thereof.

FIG. 6B illustrates an operational simulation of the photonic device inresponse to an excitation source within simulated environment 601-B, inaccordance with an embodiment of the present disclosure. In theillustrated embodiment, the photonic device is an optical demultiplexerstructures to optically separate each of a plurality of distinctwavelength channels included in a multi-channel optical signal receivedat input port 602 and respectively guide each of the plurality ofdistinct wavelength channels to a corresponding one of the plurality ofoutput regions 604. The excitation source may be selected (randomly orotherwise) from the plurality of distinct wavelength channels andoriginates at input region 602 having a specified spatial, phase, and/ortemporal profile. The operational simulation occurs over a plurality oftime steps, including the illustrated time step. When performing theoperational simulation, changes to the field response (e.g., the fieldvalue) for each of the plurality of voxels 610 are incrementally updatedin response to the excitation source over the plurality of time steps.The changes in the field response at a particular time step are based,at least in part, on the structural parameters, the excitation source,and the field response of the simulated environment 601 at theimmediately prior time step included in the plurality of time steps.Similarly, in some embodiments the source value of the plurality ofvoxels 610 is updated (e.g., based on the spatial profile and/ortemporal profile describing the excitation source). It is appreciatedthat the operational simulation is incremental and that the field values(and source values) of the simulated environment 601 are updatedincrementally at each time step as time moves forward for each of theplurality of time steps during the operational simulation. It is furthernoted that in some embodiments, the update is an iterative process andthat the update of each field and source value is based, at least inpart, on the previous update of each field and source value.

Once the operational simulation reaches a steady state (e.g., changes tothe field values in response to the excitation source substantiallystabilize or reduce to negligible values) or otherwise concludes, one ormore performance metrics may be determined. In one embodiment, theperformance metric corresponds to the power transmission at acorresponding one of the output ports 604 mapped to the distinctwavelength channel being simulated by the excitation source. In otherwords, in some embodiments, the performance metric represents power (atone or more frequencies of interest) in the target mode shape at thespecific locations of the output ports 604. A loss value or metric ofthe input design (e.g., the initial design and/or any refined design inwhich the structural parameters have been updated) based, at least inpart, on the performance metric may be determined via a loss function.The loss metric, in conjunction with an adjoint simulation, may beutilized to determine a structural gradient (e.g., influence ofstructural parameters on loss metric) for updating or otherwise revisingthe structural parameters to reduce the loss metric (i.e. increase theperformance metric). It is noted that the loss metric is further basedon a fabrication loss value that is utilized to enforce a minimumfeature size of the photonic device to promote fabricability of thedevice.

FIG. 6C illustrates an example adjoint simulation within simulatedenvironment 601-C by backpropagating a loss metric, in accordance withan embodiment of the present disclosure. More specifically, the adjointsimulation is a time-backwards simulation in which a loss metric istreated as an excitation source that interacts with the photonic deviceand causes a loss response. In other words, an adjoint (or virtualsource) based on the loss metric is placed at the output region (e.g.,output ports 604) or other location that corresponds to a location usedwhen determining the performance metric. The adjoint source(s) is thentreated as a physical stimuli or an excitation source during the adjointsimulation. A loss response of the simulated environment 601 is computedfor each of the plurality of time steps (e.g., backwards in time) inresponse to the adjoint source. The loss response collectively refers toloss values of the plurality of voxels that are incrementally updated inresponse to the adjoint source over the plurality of time steps. Thechange in loss response based on the loss metric may correspond to aloss gradient, which is indicative of how changes in the field responseof the physical device influence the loss metric. The loss gradient andthe field gradient may be combined in the appropriate way to determine astructural gradient of the photonic device/simulated environment (e.g.,how changes in the structural parameters of the photonic device withinthe simulated environment influence the loss metric). Once thestructural gradient of a particular cycle (e.g., operational and adjointsimulation) is known, the structural parameters may be updated to reducethe loss metric and generate a revised description or design of thephotonic device.

In some embodiments, iterative cycles of performing the operationalsimulation, and adjoint simulation, determining the structural gradient,and updating the structural parameters to reduce the loss metric areperformed successively as part of an inverse design process thatutilizes iterative gradient-based optimization. An optimization schemesuch as gradient descent may be utilized to determine specific amountsor degrees of changes to the structural parameters of the photonicdevice to incrementally reduce the loss metric. More specifically, aftereach cycle the structural parameters are updated (e.g., optimized) toreduce the loss metric. The operational simulation, adjoint simulation,and updating the structural parameters are iteratively repeated untilthe loss metric substantially converges or is otherwise below or withina threshold value or range such that the photonic device provides thedesired performed while maintaining fabricability.

FIG. 7A is a flow chart 700 illustrating example time steps for theoperational simulation 710 and adjoint simulation 750, in accordancewith an embodiment of the present disclosure. Flow chart 700 is onepossible implementation that a system (e.g., system 500 of FIG. 5) mayuse to perform the operational simulation 710 and adjoint simulation 750of the simulated environment (e.g., simulated environment 601 of FIGS.6A-6C) describing a photonic integrated circuit (e.g., an optical deviceoperating in an electromagnetic domain such a photonic demultiplexer).In the illustrated embodiment, the operational simulation utilizes afinite-difference time-domain (FDTD) method to model the field response(both electric and magnetic) or loss response at each of a plurality ofvoxels (e.g., plurality of voxels 610 illustrated in FIGS. 6A-6C) for aplurality of time steps in response to physical stimuli corresponding toan excitation source and/or adjoint source.

As illustrated in FIG. 7A, the flow chart 700 includes update operationsfor a portion of operational simulation 710 and adjoint simulation 750.Operational simulation 710 occurs over a plurality of time-steps (e.g.,from an initial time step to a final time step over a pre-determined orconditional number of time steps having a specified time step size) andmodels changes (e.g., from the initial field values 711) in electric andmagnetic fields of a plurality of voxels describing the simulatedenvironment and/or photonic device that collectively correspond to thefield response. More specifically, update operations (e.g., 712, 714,and 716) are iterative and based on the field response, structuralparameters 704, and one or more excitation sources 708. Each updateoperation is succeeded by another update operation, which arerepresentative of successive steps forward in time within the pluralityof time steps. For example, update operation 714 updates the fieldvalues 713 (see, e.g., FIG. 7B) based on the field response determinedfrom the previous update operation 712, sources 708, and the structuralparameters 704. Similarly, update operation 716 updates the field values715 (see, e.g., FIG. 7B) based on the field response determined fromupdate operation 714. In other words, at each time step of theoperational simulation the field values (and thus field response) areupdated based on the previous field response and structural parametersof the photonic device. Once the final time step of the operationalsimulation 710 is performed, the loss metric 718 may be determined(e.g., based on a pre-determined loss function 720). The loss gradientsdetermined from block 752 may be treated as adjoint or virtual sources(e.g., physical stimuli or excitation source originating at an outputregion or port) which are backpropagated in reverse (from the final timestep incrementally through the plurality of time steps until reachingthe initial time step) to determine structural gradient 768.

In the illustrated embodiment, the FDTD solve (e.g., operationalsimulation 710) and backward solve (e.g., adjoint simulation 750)problem are described pictorially, from a high-level, using only“update” and “loss” operations as well as their corresponding gradientoperations. The simulation is set up initially in which the structuralparameters, physical stimuli (i.e., excitation source), and initialfield states of the simulated environment (and photonic device) areprovided (e.g., via an initial description and/or input design). Asdiscussed previously, the field values are updated in response to theexcitation source based on the structural parameters. More specifically,the update operation is given by ϕ, where x_(i+1)=ϕ(x_(i),

_(i),z) for i=1, . . . , n. Here, n corresponds to the total number oftime steps (e.g., the plurality of time steps) for the operationalsimulation, where x_(i) corresponds to the field response (the fieldvalue associated with the electric and magnetic fields of each of theplurality of voxels) of the simulated environment at time step i,

_(i) corresponds to the excitation source(s) (the source valueassociated with the electric and magnetic fields for each of theplurality of voxels) of the simulated environment at time step i, and zcorresponds to the structural parameters describing the topology and/ormaterial properties of the physical device (e.g., relative permittivity,index of refraction, and the like).

It is noted that using the FDTD method, the update operation mayspecifically be stated as:ϕ(x _(i),

_(i) ,z)=A(z)x _(i) +B(z)

_(i).  (1)That is to say the FDTD update is linear with respect to the field andsource terms. Concretely, A(z)∈

^(N×N) and B(z)∈

^(N×N) are linear operators which depend on the structure parameters, z,and act on the fields, x_(i), and the sources,

_(i), respectively. Here, it is assumed that x_(i),

_(i)∈

^(N) where N is the number of FDTD field components in the operationalsimulation. Additionally, the loss operation (e.g., loss function) maybe given by L=ƒ(x_(i), . . . , x_(n)), which takes as input the computedfields and produces a single, real-valued scalar (e.g., the loss metric)that can be reduced and/or minimized.

In terms of revising or otherwise optimizing the structural parametersof the physical device, the relevant quantity to produce is

$\frac{d\; L}{dz},$which is used to describe the influence of changes in the structuralparameters on the loss value and is denoted as the structural gradient768 illustrated in FIG. 7A.

FIG. 7B is a chart 780 illustrating the relationship between the updateoperation for the operational simulation and the adjoint simulation(e.g., backpropagation), in accordance with an embodiment of the presentdisclosure. More specifically, FIG. 7B summarizes the operational andadjoint simulation relationships that are involved in computing thestructural gradient,

$\frac{d\; L}{dz},$which include

$\frac{\partial L}{\partial x_{i}},\frac{\partial x_{i + 1}}{\partial x_{i}},\frac{d\; L}{{dx}_{i}},$and

$\frac{\partial x_{i}}{\partial z}.$The update operation 714 of the operational simulation updates the fieldvalues 713, x_(i), of the plurality of voxels at the ith time step tothe next time step (i.e., i+1 time step), which correspond to the fieldvalues 715, x_(i+1). The gradients 755 are utilized to determine

$\frac{d\; L}{{dx}_{i}}$for the backpropagation (e.g., update operation 356 backwards in time),which combined with the gradients 769 are used, at least in part, tocalculate the structural gradient,

$\frac{d\; L}{dz}.$

$\frac{\partial L}{\partial x_{i}}$is the contribution of each field to the loss metric, L. It is notedthat this is the partial derivative, and therefore does not take intoaccount the causal relationship of x_(i)→x_(i+1). Thus,

$\frac{\partial x_{i + 1}}{\partial x_{i}}$is utilized which encompasses the x_(i)→x_(i+1) relationship. The lossgradient,

$\frac{d\; L}{{dx}_{i}}$may also be used to compute the structural gradient,

$\frac{d\; L}{dz},$and corresponds to the total derivative of the field with respect toloss value, L. The loss gradient,

$\frac{d\; L}{{dx}_{i}},$at a particular time step, i, is equal to the summation of

$\frac{\partial L}{\partial x_{i}} + {\frac{d\; L}{{dx}_{i + 1}}{\frac{\partial x_{i + 1}}{\partial x_{i}}.}}$Finally,

$\frac{\partial x_{i}}{\partial z},$which corresponds to the field gradient, is used which is thecontribution to

$\frac{d\; L}{dz}$from each time/update step.

In particular, the memory footprint to directly compute

$\frac{\partial L}{\partial x_{i}}$and

$\frac{d\; L}{dz}$is so large that it is difficult to store more than a handful of stateTensors. The state Tensor corresponds to storing the values of all ofthe FDTD cells (e.g., the plurality of voxels) for a single simulationtime step. It is appreciated that the term “tensor” may refer to tensorsin a mathematical sense or as described by the TensorFlow frameworkdeveloped by Alphabet, Inc. In some embodiments the term “tensor” refersto a mathematical tensor which corresponds to a multidimensional arraythat follows specific transformation laws. However, in most embodiments,the term “tensor” refers to TensorFlow tensors, in which a tensor isdescribed as a generalization of vectors and matrices to potentiallyhigher dimensions (e.g., n-dimensional arrays of base data types), andis not necessarily limited to specific transformation laws. For example,for the general loss function ƒ, it may be necessary to store thefields, x_(i), for all time steps, i. This is because, for most choicesof ƒ, the gradient will be a function of the arguments of ƒ. Thisdifficulty is compounded by the fact that the values of

$\frac{\partial L}{\partial x_{i}}$for larger values of i are needed before the values for smaller i due tothe incremental updates of the field response and/or throughbackpropagation of the loss metric, which may prevent the use of schemesthat attempt to store only the values

$\frac{\partial L}{\partial x_{i}},$at an immediate time step.

An additional difficulty is further illustrated when computing thestructural gradient,

$\frac{d\; L}{dz},$which is given by:

$\begin{matrix}{\frac{d\; L}{dz} = {\sum\limits_{i}{\frac{d\; L}{{dx}_{i}}{\frac{\partial x_{i}}{\partial z}.}}}} & (2)\end{matrix}$For completeness, the full form of the first term in the sum,

$\frac{d\; L}{dz},$is expressed as:

$\begin{matrix}{{\frac{d\; L}{{dx}_{i}} = {\frac{\partial L}{\partial x_{i}} + {\frac{d\; L}{{dx}_{i + 1}}\frac{\partial x_{i + 1}}{\partial x_{i}}}}}.} & (3)\end{matrix}$Based on the definition of ϕ as described by equation (1), it is notedthat

${\frac{\partial x_{i + 1}}{\partial x_{i}} = {A(z)}},$which can be substituted in equation (3) to arrive at an adjoint updatefor backpropagation (e.g., the update operations such as updateoperation 756), which can be expressed as:

$\begin{matrix}{{\frac{d\; L}{{dx}_{i}} = {\frac{\partial L}{\partial x_{i}} + {\frac{d\; L}{{dx}_{i + 1}}{A(z)}}}},{or}} & (4) \\{{\nabla_{x_{i}}L} = {{{A(z)}^{T}{\nabla_{x_{i + 1}}L}} + {\frac{\partial L^{T}}{\partial x_{i}}.}}} & (5)\end{matrix}$

The adjoint update is the backpropagation of the loss gradient (e.g.,from the loss metric) from later to earlier time steps and may bereferred to as a backwards solve for

$\frac{d\; L}{{dx}_{i}}.$More specifically, me loss gradient may initially be based upon thebackpropagation of a loss metric determined from the operationalsimulation with the loss function. The second term in the sum of thestructural gradient,

$\frac{d\; L}{dz},$corresponds to the field gradient and is denoted as:

$\begin{matrix}{{\frac{\partial x_{i}}{\partial z} = {\frac{d{\phi( {x_{i - 1},b_{i - 1},z} )}}{dz} = {{\frac{{dA}(z)}{dz}x_{i - 1}} + {\frac{d\;{B(z)}}{dz}b_{i - 1}}}}},} & (6)\end{matrix}$

for the particular form of ϕ described by equation (1). Thus, each termof the sum associated

$\frac{d\; L}{dz}$depends on both

$\frac{d\; L}{{dx}_{i_{0}}}$for i>=i₀ and x_(i) ₀ for i<i₀. Since the dependency chains of these twoterms are in opposite directions, it is concluded that computing

$\frac{d\; L}{dz}$in this way requires the storage of x_(i) values for all of i. In someembodiments, the need to store all field values may be mitigated by areduced representation of the fields.

FIG. 8 shows an example method 800 for generating a design of a photonicintegrated circuit, in accordance with an embodiment of the presentdisclosure. It is appreciated that method 800 is an inverse designprocess that may be accomplished by performing operations with a system(e.g., system 500 of FIG. 5) to perform iterative gradient-basedoptimization of a loss metric determined from a loss function thatincludes a performance loss and a fabrication loss. In the same or otherembodiments, method 800 may be included as instructions provided by atleast one machine-accessible storage medium (e.g., non-transitorymemory) that, when executed by a machine, will cause the machine toperform operations for generating the design of the photonic integratedcircuit. It is further appreciated that the order in which some or allof the process blocks appear in method 800 should not be deemedlimiting. Rather, one of ordinary skill in the art having the benefit ofthe present disclosure will understand that some of the process blocksmay be executed in a variety of orders not illustrated, or even inparallel.

Block 810 illustrates configuration a simulated environment to berepresentative of an initial description of a photonic integratedcircuit (e.g., photonic device) that has been received or otherwiseobtained. In some embodiments, the photonic integrated circuit may beexpected to have a certain functionality (e.g., perform as an opticaldemultiplexer) after optimization. The initial description may describestructural parameters of the photonic integrated circuit within asimulated environment. The simulated environment may include a pluralityof voxels that collectively describe the structural parameters of thephotonic device. Each of the plurality of voxels is associated with astructural value to describe the structural parameters, a field value todescribe the field response (e.g., the electric and magnetic fields inone or more orthogonal directions) to physical stimuli (e.g., one ormore excitation sources), and a source value to describe the physicalstimuli. Once the initial description has been received or otherwiseobtained, the simulated environment is configured (e.g., the number ofvoxels, shape/arrangement of voxels, and specific values for thestructural value, field value, and/or source value of the voxels are setbased on the initial description). In some embodiments the initialdescription may be a first description of the physical device in whichvalues for the structural parameters may be random values or null valuesoutside of input and output regions such that there is no bias for theinitial (e.g., first) design. It is appreciated that the initialdescription or input design may be a relative term. Thus, in someembodiments an initial description may be a first description of thephysical device described within the context of the simulatedenvironment (e.g., a first input design for performing a firstoperational simulation).

However, in other embodiments, the term initial description may refer toan initial description of a particular cycle (e.g., of performing anoperational simulation, operating an adjoint simulation, and updatingthe structural parameters). In such an embodiment, the initialdescription or design of that particular cycle may correspond to arevised description or refined design (e.g., generated from a previouscycle). In one embodiment, the simulated environment includes a designregion that includes a portion of the plurality of voxels which havestructural parameters that may be updated, revised, or otherwise changedto optimize the structural parameters of the photonic device. In thesame or other embodiments, the structural parameters are associated withgeometric boundaries and/or material compositions of the physical devicebased on the material properties (e.g., relative permittivity, index ofrefraction, etc.) of the simulated environment.

In one embodiment the simulated environment includes a design regionoptically coupled between a first communication region and a pluralityof second communication regions. In some embodiments, the firstcommunication region may correspond to an input region or port (e.g.,where an excitation source originates), while the second communicationmay correspond to a plurality of output regions or ports (e.g., whendesigning an optical demultiplexer that optically separates a pluralityof distinct wavelength channels included in a multi-channel opticalsignal received at the input port and respectively guiding each of thedistinct wavelength channels to a corresponding one of the plurality ofoutput ports). However, in other embodiments, the first communicationregion may correspond to an output region or port, while the pluralityof second communication regions corresponds to a plurality of inputports or region (e.g., when designing an optical multiplexer thatoptically combines a plurality of distinct wavelength signals receivedat respective ones of the plurality of input ports to form amulti-channel optical signal that is guided to the output port).

Block 815 shows mapping each of a plurality of distinct wavelengthchannels to a respective one of the plurality of second communicationregions. The distinct wavelength channels may be mapped to the secondcommunication regions by virtue of the initial description of thephotonic device. For example, a loss function may be chosen thatassociates a performance metric of the photonic device with powertransmission from the input port to individual output ports for mappedchannels. In one embodiment, a first channel included in the pluralityof distinct wavelength channels is mapped to a first output port,meaning that the performance metric of the photonic device for the firstchannel is tied to the first output port. Similarly, other output portsmay be mapped to the same or different channels included in theplurality of distinct wavelength channels such that each of the distinctwavelength channels is mapped to a respective one of the plurality ofoutput ports (i.e., second communication regions) within the simulatedenvironment. In one embodiment, the plurality of second communicationregions includes four regions and the plurality of distinct wavelengthchannels includes four channels that are each mapped to a correspondingone of the four regions. In other embodiments, there may be a differentnumber of the second communication regions (e.g., 8 regions) and adifferent number of channels (e.g., 8 channels) that are each mapped toa respective one of the second communication regions.

Block 820 illustrates performing an operational simulation of thephotonic integrated circuit within the simulated environment operatingin response to one or more excitation sources to determine a performancemetric. More specifically, an electromagnetic simulation is performed inwhich a field response of the photonic integrated circuit is updatedincrementally over a plurality of time steps to determine how the howthe field response of the physical device changes due to the excitationsource. The field values of the plurality of voxels are updated inresponse to the excitation source and based, at least in part, on thestructural parameters of the integrated photonic circuit. Additionally,each update operation at a particular time step may also be based, atleast in part, on a previous (e.g., immediately prior) time step.

Consequently, the operational simulation simulates an interactionbetween the photonic device (i.e., the photonic integrated circuit) anda physical stimuli (i.e., one or more excitation sources) to determine asimulated output of the photonic device (e.g., at one or more of theoutput ports or regions) in response to the physical stimuli. Theinteraction may correspond to any one of, or combination of aperturbation, retransmission, attenuation, dispersion, refraction,reflection, diffraction, absorption, scattering, amplification, orotherwise of the physical stimuli within electromagnetic domain due, atleast in part, to the structural parameters of the photonic device andunderlying physics governing operation of the photonic device. Thus, theoperational simulation simulates how the field response of the simulatedenvironment changes due to the excitation source over a plurality oftime steps (e.g., from an initial to final time step with apre-determined step size).

In some embodiments, the simulated output may be utilized to determineone or more performance metrics of the photonic integrated circuit. Forexample, the excitation source may correspond to a selected one of aplurality of distinct wavelength channels that are each mapped to one ofthe plurality of output ports. The excitation source may originate at orbe disposed proximate to the first communication region (i.e., inputport) when performing the operational simulation. During the operationalsimulation, the field response at the output port mapped to the selectedone of the plurality of distinct wavelength channels may then beutilized to determine a simulated power transmission of the photonicintegrated circuit for the selected distinct wavelength channel. Inother words, the operational simulation may be utilized to determine theperformance metric that includes determining a simulated powertransmission of the excitation source from the first communicationregion, through the design region, and to a respective one of theplurality of second communication regions mapped to the selected one ofthe plurality of distinct wavelength channels. In some embodiments, theexcitation source may cover the spectrum of all of the plurality ofoutput ports (e.g., the excitation source spans at least the targetedfrequency ranges for the bandpass regions for each of the plurality ofdistinct wavelength channels as well as the corresponding transitionband regions, and at least portions of the corresponding stopbandregions) to determine a performance metric (i.e., simulated powertransmission) associated with each of the distinct wavelength channelsfor the photonic integrated circuit. In some embodiments, one or morefrequencies that span the passband of a given one of the plurality ofdistinct wavelength channels is selected randomly to optimize the design(e.g., batch gradient descent while having a full width of each passbandincluding ripple in the passband that meets the target specifications).In the same or other embodiments, each of the plurality of distinctwavelength channels has a common bandwidth with different centerwavelengths.

Block 825 shows determining a loss metric based on a performance lossassociated with a performance metric and a fabrication loss associatedwith a minimum feature size. In some embodiments the loss metric isdetermined via a loss function that includes both the performance lossand the fabrication loss as input values. The performance loss maycorrespond to a difference between the performance metric and a targetperformance metric of the photonic integrated circuit. In someembodiments, a minimum feature size for the design region of thesimulated environment may be provided to promote fabricability of thedesign generated by the inverse design process. The fabrication loss isbased, at least in part, on the minimum feature size and the structuralparameters of the design region. More specifically, the fabrication lossenforces the minimum feature size for the design such that the designregion does not have structural elements with a diameter less than theminimum feature size. This helps this system provide designs that meetcertain fabricability and/or yield requirements. In some embodiments thefabrication loss also helps enforce binarization of the design (i.e.,rather than mixing the first and second materials together to form athird material, the design includes regions of the first material andthe second material that are inhomogeneously interspersed).

In some embodiments the fabrication loss is determined by generating aconvolution kernel (e.g., circular, square, octagonal, or otherwise)with a width equal to the minimum feature size. The convolution kernelis then shifted through the design region of the simulated environmentto determine voxel locations (i.e., individual voxels) within the designregion that fit the convolution kernel within the design region withoutextending beyond the design region. The convolution kernel is thenconvolved at each of the voxel locations with the structural parametersassociated with the voxel locations to determine first fabricationvalues. The structural parameters are then inverted and the convolutionkernel is convolved again at each of the voxel locations with theinverted structural parameters to determine second fabrication values.The first and second fabrication values are subsequently combined todetermine the fabrication loss for the design region. This process ofdetermining the fabrication loss may promote structural elements of thedesign region having a radius of curvature less having a magnitude ofless than a threshold size (i.e., inverse of half the minimum featuresize).

Block 830 illustrates backpropagating the loss metric via the lossfunction through the simulated environment to determine an influence ofchanges in the structural parameters on the loss metric (i.e.,structural gradient). The loss metric is treated as an adjoint orvirtual source and is backpropagated incrementally from a final timestep to earlier time steps in a backwards simulation to determine thestructural gradient of the photonic integrated circuit.

Block 835 shows revising a design of the photonic integrated circuit(e.g., generated a revised description) by updating the structuralparameters to adjust the loss metric. In some embodiments, adjusting forthe loss metric may reduce the loss metric. However, in otherembodiments, the loss metric may be adjusted or otherwise compensated ina manner that does not necessarily reduce the loss metric, In oneembodiment, adjusting the loss metric may maintain fabricability whileproviding a general direction within the parameterization space toobtain designs that will ultimately result in increased performancewhile also maintaining device fabricability and targeted performancemetrics. In some embodiments, the revised description is generated byutilizing an optimization scheme after a cycle of operational andadjoint simulations via a gradient descent algorithm, Markov Chain MonteCarlo algorithm, or other optimization techniques. Put in another way,iterative cycles of simulating the photonic integrated circuit,determining a loss metric, backpropagating the loss metric, and updatingthe structural parameters to adjust the loss metric may be successivelyperformed until the loss metric substantially converges such that thedifference between the performance metric and the target performancemetric is within a threshold range while also accounting forfabricability and binarization due to the fabrication loss. In someembodiments, the term “converges” may simply indicate the difference iswithin the threshold range and/or below some threshold value.

Block 840 illustrates determining whether the loss metric substantiallyconverges such that the difference between the performance metric andthe target performance metric is within a threshold range. Iterativecycles of simulating the photonic integrated circuit with the excitationsource selected from the plurality of distinct wavelength channels,backpropagating the loss metric, and revising the design by updating thestructural parameters to reduce the loss metric until the loss metricsubstantially converges such that the difference between the performancemetric and the target performance metric is within a threshold range. Insome embodiments, the structural parameters of the design region of theintegrated photonic circuit are revised when performing the cycles tocause the design region of the photonic integrated circuit to opticallyseparate each of the plurality of distinct wavelength channels from amulti-channel optical signal received via the first communication regionand guide each of the plurality of distinct wavelength channels to thecorresponding one of the plurality of second communication regions basedon the mapping of block 815.

Block 845 illustrates outputting an optimized design of the photonicintegrated circuit in which the structural parameters have been updatedto have the difference between the performance metric and the targetperformance metric within a threshold range while also enforcing aminimum feature size and binarization.

The processes explained above are described in terms of computersoftware and hardware. The techniques described may constitutemachine-executable instructions embodied within a tangible ornon-transitory machine (e.g., computer) readable storage medium, thatwhen executed by a machine will cause the machine to perform theoperations described. Additionally, the processes may be embodied withinhardware, such as an application specific integrated circuit (“ASIC”) orotherwise.

A tangible machine-readable storage medium includes any mechanism thatprovides (i.e., stores) information in a non-transitory form accessibleby a machine (e.g., a computer, network device, personal digitalassistant, manufacturing tool, any device with a set of one or moreprocessors, etc.). For example, a machine-readable storage mediumincludes recordable/non-recordable media (e.g., read only memory (ROM),random access memory (RAM), magnetic disk storage media, optical storagemedia, flash memory devices, etc.).

The above description of illustrated embodiments of the invention,including what is described in the Abstract, is not intended to beexhaustive or to limit the invention to the precise forms disclosed.While specific embodiments of, and examples for, the invention aredescribed herein for illustrative purposes, various modifications arepossible within the scope of the invention, as those skilled in therelevant art will recognize.

These modifications can be made to the invention in light of the abovedetailed description. The terms used in the following claims should notbe construed to limit the invention to the specific embodimentsdisclosed in the specification. Rather, the scope of the invention is tobe determined entirely by the following claims, which are to beconstrued in accordance with established doctrines of claiminterpretation.

What is claimed is:
 1. A multi-channel photonic demultiplexer,comprising: an input region to receive a multi-channel optical signalincluding four distinct wavelength channels; four output regions, eachto receive a corresponding one of the four distinct wavelength channelsdemultiplexed from the multi-channel optical signal; and a dispersiveregion optically disposed between the input region and the four outputregions, wherein the dispersive region includes a first material and asecond material inhomogeneously interspersed to form a plurality ofinterfaces that each correspond to a change in refractive index of thedispersive region and collectively structure the dispersive region tooptically separate each of the four distinct wavelength channels fromthe multi-channel optical signal and respectively guide each of the fourdistinct wavelength channels to the corresponding one of the four outputregions when the input region receives the multi-channel optical signal,wherein the plurality of interfaces forms a material interface patternalong a cross-sectional area of the dispersive region that is at leastpartially surrounded by a periphery region that includes the secondmaterial, wherein the material interface pattern includes a plurality ofislands, wherein a first island included in the plurality of islands isformed of the first material and surrounded by the second material, andwherein a second island included in the plurality of islands is formedof the second material and surrounded by the first material.
 2. Themulti-channel photonic demultiplexer of claim 1, wherein the firstmaterial and the second material are arranged within the dispersiveregion such that the material interface pattern along thecross-sectional area of the dispersive region is shaped substantiallyproportional to interface pattern “431” as illustrated in FIG. 4B. 3.The multi-channel photonic demultiplexer of claim 1, wherein thematerial interface pattern includes protrusions, formed of the secondmaterial, that extend from the periphery region into the dispersiveregion.
 4. The multi-channel photonic demultiplexer of claim 1, whereinthe material interface pattern includes one or more dendritic shapes,wherein each of the one or more dendritic shapes are defined as abranched structure formed from the first material or the second materialand having a width that alternates between increasing and decreasing insize along a corresponding direction.
 5. The multi-channel photonicdemultiplexer of claim 1, wherein the first material and the secondmaterial are arranged and shaped within the dispersive region such thatthe material interface pattern is substantially proportional to a designobtainable with an inverse design process.
 6. The multi-channel photonicdemultiplexer of claim 5, wherein the inverse design process includesiterative optimization of the design based, at least in part, on a lossfunction that incorporates a performance loss and a fabrication lossthat is adjusted via the iterative optimization to generate the design.7. The multi-channel photonic demultiplexer of claim 1, wherein thedispersive region is further structured to optically separate each ofthe four distinct wavelength channels from the multi-channel opticalsignal within a predetermined area of 100 μm×100 μm or less when theinput region receives the multi-channel optical signal.
 8. Themulti-channel photonic demultiplexer of claim 1, wherein the dispersiveregion is structured to accommodate a common bandwidth for each of thefour distinct wavelength channels, each having different centerwavelengths, wherein the common bandwidth is approximately 13 nm wide,and wherein the different center wavelengths include at least one of1271 nm, 1291 nm, 1311 nm, 1331 nm, 1511 nm, 1531 nm, 1551 nm, or 1571nm.
 9. The multi-channel photonic demultiplexer of claim 1, wherein thematerial interface pattern is shaped to enforce a minimum feature sizewithin the dispersive region such that the plurality of interfaceswithin the cross-sectional area formed from the first material andsecond material do not have at least one of a radius of curvature with amagnitude of less than a first threshold size, a minimum width of lessthan a second threshold size, or a minimum spacing of less than a thirdthreshold size.
 10. The multi-channel photonic demultiplexer of claim 1,wherein the dispersive region is structured to have a power transmissionof −2 dB or greater from the input region, through the dispersiveregion, and to the corresponding one of the four output regions for agiven wavelength within one of the four distinct wavelength channels.11. The multi-channel photonic demultiplexer of claim 10, wherein thedispersive region is further structured to have at least one of anadverse power transmission for the given wavelength from the inputregion to any of the four output regions other than the correspondingone of the four output regions is −30 dB or less, ripple within abandpass region of each of the four distinct wavelength channels is 1 dBor less, or a maximum power reflection of the multi-channel opticalsignal is −40 dB or less.
 12. The multi-channel photonic demultiplexerof claim 1, wherein the dispersive region includes a first side and asecond side opposite the first side, wherein the input region isdisposed proximate to the first side, wherein the four output regionsare disposed proximate to the second side, and wherein each one of thefour output regions is positioned parallel to each other one of the fouroutput regions.
 13. The multi-channel photonic demultiplexer of claim12, wherein adjacent pairs of the four output regions are separated fromeach other by a common separation distance.
 14. At least onemachine-accessible storage medium that provides instructions that, whenexecuted by a machine, will cause the machine to perform operations forgenerating a design of a photonic integrated circuit, the operationscomprising: configuring a simulated environment to be representative ofan initial description of the photonic integrated circuit, wherein thesimulated environment includes a design region optically coupled betweena first communication region and a plurality of second communicationregions, wherein the plurality of second communication regions includesfour communication regions, and wherein the design region is defined bystructural parameters of the simulated environment; mapping each of fourdistinct wavelength channels to a respective one of the fourcommunication regions; performing an operational simulation of thephotonic integrated circuit within the simulated environment in responseto an excitation source corresponding to a selected one of the fourdistinct wavelength channels to determine a performance metric of thephotonic integrated circuit; determining a loss metric based, at leastin part, on a difference between the performance metric and a targetperformance metric of the photonic integrated circuit; backpropagatingthe loss metric through the simulated environment to determine astructural gradient corresponding to an influence of changes in thestructural parameters on the loss metric; revising the design of thephotonic integrated circuit by updating the structural parameters toadjust the loss metric based, at least in part, on the structuralgradient; and iteratively performing cycles of simulating the photonicintegrated circuit with the excitation source selected from the fourdistinct wavelength channels, backpropagating the loss metric, andrevising the design by updating the structural parameters to adjust theloss metric until the loss metric substantially converges such that thedifference between the performance metric and the target performancemetric is within a threshold range.
 15. The at least onemachine-accessible storage medium of claim 14, wherein the excitationsource originates at or is disposed proximate to the first communicationregion when performing the operational simulation.
 16. The at least onemachine-accessible storage medium of claim 15, wherein determining theperformance metric further includes determining a simulated powertransmission of the excitation source from the first communicationregion, through the design region, and to the respective one of the fourcommunication regions mapped to the selected one of the four distinctwavelength channels when performing the operational simulation.
 17. Theat least one machine-accessible storage medium of claim 16, thatprovides additional instructions that, when executed by the machine,will cause the machine to perform further operations including:determining additional simulated power transmission of the excitationsource from the first communication region, through the design region,and to each other one of the four communication regions than therespective one of the four communication regions mapped to the selectedone of the four distinct wavelength channels to determine isolation ofthe excitation source.
 18. The at least one machine-accessible storagemedium of claim 14, wherein one or more wavelengths within a bandpassregion of each of the four distinct wavelength channels is selectedrandomly for performing the operational simulation, and wherein each ofthe plurality of distinct wavelength channels have a common bandwidthwith different center wavelengths.
 19. The at least onemachine-accessible storage medium of claim 14, that provides additionalinstructions that, when executed by the machine, will cause the machineto perform further operations including: providing a minimum featuresize for the design region of the simulated environment; and determininga fabrication loss based on the minimum feature size, wherein the lossmetric is based, at least in part, on the fabrication loss, and whereinthe fabrication loss enforces the minimum feature size for the designsuch that the design region does not have structural elements with awidth or spacing less than the minimum feature size.
 20. The at leastone machine-accessible storage medium of claim 19, wherein determiningthe fabrication loss includes: generating a convolution kernel with awidth equal to the minimum feature size; shifting the convolution kernelthrough the design region of the simulated environment to determinevoxel locations within the design region that fit the convolution kernelwithin the design region without extending beyond the design region;convolving the convolution kernel at each of the voxel locations withthe structural parameters associated with the voxel locations todetermine first fabrication values; inverting the structural parametersand convolving the convolution kernel at each of the voxel locationswith the inverted structural parameters to determine second fabricationvalues; and combining the first fabrication values and the secondfabrication values to determine the fabrication loss for the designregion.
 21. The at least one machine-accessible storage medium of claim14, wherein the structural parameters of the design region of theintegrated photonic circuit are revised when performing the cycles tocause the design region of the photonic integrated circuit to opticallyseparate each of the four distinct wavelength channels from amulti-channel optical signal received via the first communication regionand guide each of the four distinct wavelength channels to thecorresponding one of the plurality of second communication regions basedon the mapping.
 22. At least one machine-accessible storage medium thatprovides instructions that, when executed by a machine, will cause themachine to perform operations for generating a design of a photonicintegrated circuit, the operations comprising: configuring a simulatedenvironment to be representative of an initial description of thephotonic integrated circuit, wherein the simulated environment includesa design region optically coupled between a first communication regionand a plurality of second communication regions, wherein the pluralityof second communication regions includes four communication regions, andwherein the design region is defined by structural parameters of thesimulated environment; mapping each of four distinct wavelength channelsto a respective one of the four communication regions; performing anoperational simulation of the photonic integrated circuit within thesimulated environment in response to an excitation source correspondingto a selected one of the four distinct wavelength channels to determinea performance metric of the photonic integrated circuit, wherein one ormore wavelengths within a bandpass region of each of the four distinctwavelength channels is selected randomly for performing the operationalsimulation, and wherein each of the plurality of distinct wavelengthchannels have a common bandwidth with different center wavelengths;determining a loss metric based, at least in part, on a differencebetween the performance metric and a target performance metric of thephotonic integrated circuit; backpropagating the loss metric through thesimulated environment to determine a structural gradient correspondingto an influence of changes in the structural parameters on the lossmetric; and revising the design of the photonic integrated circuit byupdating the structural parameters to adjust the loss metric based, atleast in part, on the structural gradient.
 23. At least onemachine-accessible storage medium that provides instructions that, whenexecuted by a machine, will cause the machine to perform operations forgenerating a design of a photonic integrated circuit, the operationscomprising: configuring a simulated environment to be representative ofan initial description of the photonic integrated circuit, wherein thesimulated environment includes a design region optically coupled betweena first communication region and a plurality of second communicationregions, wherein the plurality of second communication regions includesfour communication regions, and wherein the design region is defined bystructural parameters of the simulated environment; mapping each of fourdistinct wavelength channels to a respective one of the fourcommunication regions; performing an operational simulation of thephotonic integrated circuit within the simulated environment in responseto an excitation source corresponding to a selected one of the fourdistinct wavelength channels to determine a performance metric of thephotonic integrated circuit; determining a loss metric based, at leastin part, on a difference between the performance metric and a targetperformance metric of the photonic integrated circuit; providing aminimum feature size for the design region of the simulated environment;and determining a fabrication loss based on the minimum feature size,wherein the loss metric is based, at least in part, on the fabricationloss, and wherein the fabrication loss enforces the minimum feature sizefor the design such that the design region does not have structuralelements with a width or spacing less than the minimum feature size;backpropagating the loss metric through the simulated environment todetermine a structural gradient corresponding to an influence of changesin the structural parameters on the loss metric; and revising the designof the photonic integrated circuit by updating the structural parametersto adjust the loss metric based, at least in part, on the structuralgradient.
 24. The at least one machine-accessible storage medium ofclaim 23, wherein determining the fabrication loss includes: generatinga convolution kernel with a width equal to the minimum feature size;shifting the convolution kernel through the design region of thesimulated environment to determine voxel locations within the designregion that fit the convolution kernel within the design region withoutextending beyond the design region; convolving the convolution kernel ateach of the voxel locations with the structural parameters associatedwith the voxel locations to determine first fabrication values;inverting the structural parameters and convolving the convolutionkernel at each of the voxel locations with the inverted structuralparameters to determine second fabrication values; and combining thefirst fabrication values and the second fabrication values to determinethe fabrication loss for the design region.